Problem: $g(x) = -2x^{2}+f(x)$ $f(t) = 7t^{3}-5t^{2}+7t-6+2(h(t))$ $h(n) = -n^{3}-5n^{2}$ $ h(f(0)) = {?} $
Answer: First, let's solve for the value of the inner function, $f(0)$ . Then we'll know what to plug into the outer function. $f(0) = 7(0^{3})-5(0^{2})+(7)(0)-6+2(h(0))$ To solve for the value of $f$ , we need to solve for the value of $h(0)$ $h(0) = -0^{3}-5(0^{2})$ $h(0) = 0$ That means $f(0) = 7(0^{3})-5(0^{2})+(7)(0)-6+(2)(0)$ $f(0) = -6$ Now we know that $f(0) = -6$ . Let's solve for $h(f(0))$ , which is $h(-6)$ $h(-6) = -(-6)^{3}-5(-6)^{2}$ $h(-6) = 36$